Precise subtyping for asynchronous multiparty sessions

Silvia Ghilezan, Jovanka Pantović, Ivan Prokić, Alceste Scalas, Nobuko Yoshida

Research output: Contribution to journalArticlepeer-review


Session subtyping is a cornerstone of refinement of communicating processes: a process implementing a session type (i.e., a communication protocol) T can be safely used whenever a process implementing one of its supertypes T′ is expected, in any context, without introducing deadlocks nor other communication errors. As a consequence, whenever T T′ holds, it is safe to replace an implementation of T′ with an implementation of the subtype T, which may allow for more optimised communication patterns.

We present the first formalisation of the precise subtyping relation for asynchronous multiparty sessions. We show that our subtyping relation is sound (i.e., guarantees safe process replacement, as outlined above) and also complete: any extension of the relation is unsound. To achieve our results, we develop a novel session decomposition technique, from full session types (including internal/external choices) into single input/output session trees (without choices).

Previous work studies precise subtyping for binary sessions (with just two participants), or multiparty sessions (with any number of participants) and synchronous interaction. Here, we cover multiparty sessions with asynchronous interaction, where messages are transmitted via FIFO queues (as in the TCP/IP protocol), and prove that our subtyping is both operationally and denotationally precise. In the asynchronous multiparty setting, finding the precise subtyping relation is a highly complex task: this is because, under some conditions, participants can permute the order of their inputs and outputs, by sending some messages earlier or receiving some later, without causing errors; the precise subtyping relation must capture all such valid permutations — and consequently, its formalisation, reasoning and proofs become challenging. Our session decomposition technique overcomes this complexity, expressing the subtyping relation as a composition of refinement relations between single input/output trees, and providing a simple reasoning principle for asynchronous message optimisations.
Original languageEnglish
Article number16
Pages (from-to)1-28
Number of pages28
JournalProceedings of the ACM on Programming Languages
Issue numberPOPL
Publication statusPublished - 4 Jan 2021

Bibliographical note

© 2021 Copyright held by the owner/author(s). This work is licensed under a Creative Commons Attribution-Share Alike 4.0 International License.

Funding: EU Horizon 2020 project 830929 (łCyberSec4Europež); EU COST Actions
CA15123 (łEUTypesž) and IC1201 (łBETTYž); EPSRC EP/T006544/1, EP/K011715/1, EP/K034413/1,
EP/L00058X/1, EP/N027833/1, EP/N028201/1, EP/T006544/1, EP/T014709/1 and EP/V000462/1, and
NCSS/EPSRC VeTSS; MPNTR and SFRS #6526707 (łAI4TrustBCž).


  • asynchronous multiparty session types
  • completeness
  • pi-calculus
  • session types
  • soundness
  • subtyping
  • typing systems


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